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QUANTUM IMAGING This field exploits the quantum nature of light and the natural parallelism of optical signals to devise novel techniques for optical imaging and for parallel information processing at the quantum level.

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Brambilla, Gatti, Bache and Lugiato, Phys. Rev. A 69, 023802 (2004) SIGNAL IDLER Finite size of the pump waist w P --> uncertainty in the propagation directions of twin photons uncertainty in the transverse momentum of photon 1 from a measurement of the momentum of photon 2 Perfect intensity correlation recovered for detection areas larger than l c =5mm SIGNAL IDLER  (2) NEAR FIELD FAR FIELD Finite crystal length--> uncertainty in the twin photon position due to diffraction spread uncertainty in the position of photon 1 from a measurement of the position of photon 2 Perfect spatial intensity correlation for detection areas larger than pump

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Ordinary twin beams: but uncorrelated in space photon number correlated in time, but uncorrelated in space i 1 (t) i 2 (t) i 3 (t) i 3 ’ (t) i 2 ’ (t) i 1 ’ (t) i 1 (t) i 2 (t) i 3 (t) i 3 ’ (t) i 2 ’ (t) i 1 ’ (t) Spatially entangled beams: and in the beam cross sections photon numbers correlated in time and in the beam cross sections

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No interference filter during measurements to reduce the transmission losses Spatial area used for statistics selected around degeneracy Photocounts (signal-idler) difference statistics of pixel pairs Quantity evaluated over single shot: Averages are only SPATIAL performed inside box (~4000 pixels).

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Detection of a weak absorption (e.g. a spectroscopic signal): typically a differential measurement is used Weak absorbtion 1 2 N 2 -N 1  signal BS This schemes suppresses the excess noise in the incoming beam, but is affected by the shot noise in N 2 -N 1 By using single-mode twin beams produced by cw optical parametric oscillators  improvement in the signal to noise-ratio: Souto Ribeiro, Schwob, Maitre, Fabre, Opt. Lett. 22, 1893 (1997):1.9 dB; Jiangrui Gao et al., Opt.Lett. 23, 870 (1998):7dB In the far field of the PDC emission: twin beam effect over several phase conjugate signal and idler modes  Can be used to enhance the sensitivity of detection of weak images: useful e.g. in biological imaging or whenever there is the need of illuminating the object with ultra-low light intensity.

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Field generated by single pass parametric down-conversion, or by optical parametric oscillators with mode-degenerate cavities i 1 (t) i 2 (t) + - x O In the crystal, each generated parametric photon has its “twin” produced in a symmetric direction noise reduced on the intensity difference Parametric medium USE OF SPATIAL ENTANGLEMENT

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Possibility of performing coherent imaging using incoherent light Two arm configuration: more flexibility in comparison with standard imaging illuminating the object with one frequency and detecting the light at an other frequency image processing by only operating on the optics in the reference arm 2

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2f-2f scheme:ghost image 10000 SHOTS f-f scheme:ghost diffraction 10000 SHOTS By only operating on the optical set-up in the path of beam 2 (which never went through the object), one is able to pass from the interference pattern to the image of the object. Key point: simultaneous presence of spatial correlation both in the near and in the far- field of the PDC beams. Feature that distinguishes the entangled from the classical source ? reference beam 2 test beam 1  (2) ff ff x reference beam 2 test beam 1  (2) ff 2f x DOUBLE SLIT

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First guess: it is not possible to realize both the ghost image and the ghost diffraction experiment using the same classical source

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Gatti Brambilla Bache Lugiato, PRL 93, 093602 (2004), Phys. Rev. A 70, 013802 (2004), quant-phys/0307187 (2003). A surprising answer : b1b1 b2b2 vacuum 50:50 BS Beam in a thermal-like state N1N1 N2N2 Nothing prevents two classical beams from being spatially correlated both in the near and in the far field up to an imperfect degree (i.e. classically, or at shot noise) A spatially incoherent thermal-like beam divided on a beam splitter generates two spatially correlated beams that can be used for ghost imaging exactly in the same way as the entangled beams, with the only exception of the visibility.

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An old favourite of the 70-ties: the speckle pattern generated by impinging a laser beam on a ground glass LASER BS ROTATING GROUND GLASS TO CCD Splitting symmetrically: “twin” speckle patterns If the cross-section is much larger than the speckle size, the spatial correlation is preserved upon propagation (Van Cittert-Zernike): high degree of (classical) spatial correlation both in the near and far zones.

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The only difference from an entangled source is a lower visibility of the information. This feature, however, does not prevent from retrieving the image (ore the diffraction pattern), unless the object is too weak. Entanglement can be advantageous in high sensitivity measurements (e.g. imaging of a faint object or in quantum information (e.g. cryptographic) schemes, no evident practical advantages in imaging macroscopic classical objects.

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In the case of a pure amplitude object, such as a double slit, the diffraction pattern can be observed using the well known Hanbury - Brown and Twiss technique. In this way one obtains the Fourier transform of the modulus square of the object. In the case of a double slit, this coincides with the Fourier transform of the object. But in presence of phase modulation in the object, this is lost in the measurement. This is equivalent to measuring the spatial autocorrelation of the field transmitted by the object BS OBJECT Thermal light Far field

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In this case, one obtains the Fourier transform of the object even in the presence of phase modulation. Hence this is truly coherent imaging with incoherent light. Cross- correlation Auto-correlation BS OBJECT Thermal light BS OBJECT Thermal light Far field GHOST IMAGING TECHNIQUE HBT TECHNIQUE

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USEFULNESS FOR QUANTUM INFORMATION AND COMMUNICATION VERY LARGE NUMBER OF ENTANGLED SPATIAL MODES (“CONTINUOUS VARIABLES” ENTANGLEMENT) ONE HAS A VERY LARGE NUMBER OF REPLICAS OF THE SAME SYSTEM (PAIR OF ENTANGLED SPATIAL MODES) IN A SINGLE PUMP PULSE. THIS PROVIDES A PARALLEL (“FAX”) CONFIGURATION FOR QUANTUM INFORMATION PROCESSING, ALTERNATIVE TO THE SEQUENTIAL (‘TELEPHONE”) CONFIGURATION OF THE REGIME IN WHICH ONE DETECTS SINGLE ENTANGLED PHOTON PAIRS.